Single-Phase LXe Proportional Scintillation

• Single-phase LXe proportional scintillation is a process in which ionization electrons in liquid xenon are accelerated by high electric fields near thin electrodes to excite xenon atoms and emit VUV photons.
• It operates entirely within the liquid phase, delivering photon yields typically between 10 and 30 photons/e⁻ above a threshold of ~412 kV/cm while simplifying detector mechanics.
• The technique offers rapid S2 pulse timing and improved scalability for dark matter and neutrino experiments, despite challenges such as field-induced instabilities and mechanical constraints.

Single-phase proportional scintillation in liquid xenon (LXe) is the process by which ionization electrons, liberated by particle interactions in the LXe bulk, are drifted toward regions of extremely high electric field—typically in the vicinity of thin wires or needle-shaped electrodes—where they excite xenon atoms to produce vacuum ultraviolet (VUV) photons. This secondary, field-induced photon emission, known as proportional scintillation or electroluminescence, enables conversion of the ionization charge signal into an optical (S2) signal for detection and analysis. Unlike traditional dual-phase time projection chambers (TPCs), which require extraction of electrons from liquid into the gas for proportional scintillation, the single-phase approach achieves this entirely within the liquid, offering distinct mechanical, operational, and scaling advantages at the expense of higher required local fields and engineering challenges. The characteristic thresholds, photon yields, width and topology of the S2 pulses, and the practical design constraints are governed by the microscopic physics of electron excitation, the electrode geometry, and the interplay between S2 gain and field-induced instabilities.

1. Physical Mechanism and Scintillation Thresholds

Single-phase LXe proportional scintillation relies on the excitation (but not full ionization) of xenon atoms by electrons accelerated in high electric fields. The threshold for proportional scintillation in LXe is sharply defined: electroluminescence begins when the local field exceeds $E_\text{thr,S2} = 412^{+10}_{-133}\,\text{kV/cm}$, as determined by Aprile et al. in systematic wire-based studies (Aprile et al., 2014). Above this threshold, each electron gains sufficient kinetic energy between collisions to excite Xe atoms—populating Xe* and subsequently Xe$_2^*$ excimer states, which decay emitting $\sim 175$ nm VUV photons (Kuger et al., 2021, Tönnies et al., 2024). At yet higher fields, above $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$, impact ionization initiates electron multiplication, increasing the S2 yield but also introducing excess fluctuations (Aprile et al., 2014, Juyal et al., 2019, Juyal et al., 2021).

This process is confined to micron-scale regions adjacent to the amplification structures (e.g., near 10–50 µm diameter wires or needle tips), where the electric field scales as $E(r) = V_A / [r\ln(b/a)]$—with rapid 1/r divergence at small radii (Aprile et al., 2014, Qi et al., 2023, Wei et al., 2021).

2. Electrode Geometries and Electric Field Implementation

Proportional scintillation in liquid xenon is typically realized using:

• Thin anode wires (diameters 5–50 µm): Deployed in parallel planes (as in MWPC-style grids) for planar TPCs (Aprile et al., 2014, Tönnies et al., 2024, Juyal et al., 2021, Juyal et al., 2019).
• Central axial wires: Used in radial TPCs for cylindrical symmetry (Wei et al., 2021).
• Needle-like electrodes: Chemically etched tungsten needles with $\lesssim 50$ µm tip radius, enabling fields $\gtrsim$ MV/cm at moderate voltages (Knights et al., 2024).

Table: Typical geometry and threshold values

Geometry type	Electrode size	S2 threshold field	Max S2 yield (ph/e⁻)
Thin wire (planar)	10 µm	$\sim$410 kV/cm	$287^{+97}_{-75}$*
Thin wire (radial)	25 µm	$\sim$400 kV/cm	$_2^*$0
Needle	50 µm tip	$_2^*$1800 kV/cm	$_2^*$2

*Including moderate avalanche at high field (Aprile et al., 2014).

Wire diameter and applied voltage set the maximum achievable surface field and gain, subject to constraints from field emission and dark discharge.

3. Scintillation Gains, Pulse Characteristics, and Readout

The photon yield in the pure proportional regime rises approximately linearly with field above threshold:

$_2^*$3

where $_2^*$4 is an empirical proportionality factor (Aprile et al., 2014, Kuger et al., 2021, Tönnies et al., 2024). Total S2 yields in pure proportional mode (i.e., below avalanche onset) are consistently reported as $_2^*$5–$_2^*$6 photons/e⁻ for 10–25 µm wires at fields just above threshold, e.g.:

• $_2^*$7 photons/e⁻ at $_2^*$8 on a 10 µm wire (Tönnies et al., 2024).
• $_2^*$9 photons/e⁻ for a 10 µm wire at 3.6 kV (Qi et al., 2023).
• $\sim 175$0 photons/e⁻ in multiwire MWPC geometries (Juyal et al., 2019, Juyal et al., 2021).

In the moderate avalanche regime (approaching 725 kV/cm), gains up to $\sim 175$1 photons/e⁻ and net charge gain $\sim 175$2 are observed, but excess stochasticity degrades energy resolution (Aprile et al., 2014).

Pulse widths for single-phase S2 signals are distinctly narrow: the de-excitation time of Xe$\sim 175$3 triplet states (27 ns) sets a lower bound, with observed S2 pulse widths $\sim 175$4 ns for single electrons at minimal drift, growing via diffusion for longer drifts (Tönnies et al., 2024). By contrast, dual-phase S2 widths (in the gas gap) are typically $\sim 175$5s.

S2 gains for needle geometry also approach $\sim 175$6 photons/e⁻ at tip fields above 1 MV/cm, scaling exponentially with voltage (Knights et al., 2024).

4. Signal Discrimination, Energy Resolution, and Scaling

Single-phase proportional scintillation enables S1+S2 or S2-only analysis. The combined energy scale is constructed as:

$\sim 175$7

with $\sim 175$8 and $\sim 175$9 denoting light collection and S2 gains, calibrated from known lines (Qi et al., 2023, Qi et al., 2024). While $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$0 is typically an order of magnitude smaller than dual-phase modes, electron-counting is feasible for $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$1 PE/e⁻ (Tönnies et al., 2024, Kuger et al., 2021).

Discrete electron counting with O(100 ns) S2 pulses enables robust pile-up rejection, improved single-site/multisite discrimination (e.g., neutron multiple-scatter rejection efficiency of 93% at 98% acceptance in DARWIN-scale analyses) (Kuger et al., 2021). For $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$2, energy resolution improves by $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$3 versus dual-phase due to reduction in detection/diffusion errors; at higher energies the resolution approaches the Fano limit set by primary ionization fluctuations (Kuger et al., 2021, Qi et al., 2023).

Spatial reconstruction is possible via S2 pulse-width diffusion, yielding $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$4-resolution scaling as $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$5 (Kuger et al., 2021). The absence of a liquid-gas interface avoids extraction inefficiency and related backgrounds, although single-electron "train" backgrounds are not mitigated by single-phase operation (Qi et al., 2024).

5. Electrode Effects, Light Collection, and Field Engineering

Extensive finite-element modeling confirms that fields around 10–20 µm wires at few kV bias fulfill the proportional regime requirements. Electrons are funneled into narrow angular cones ($E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$6–$E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$7 total width), with shadowing effects from the wires primarily geometric: for 20 µm wires, $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$837% of S2 photons are shadowed, but 30% of these are reflected by gold plating, leading to net detection efficiencies of 74% for normal-incidence PMT arrays (Juyal et al., 2021).

Scalability to ton-scale detectors leverages multi-plane wire arrays (with $E_\text{thr,mult} = 725^{+48}_{-139}\,\text{kV/cm}$91 kV/cm drift field, 10–20 µm wires at millimeter pitch, and per-plane voltages $E(r) = V_A / [r\ln(b/a)]$05–10 kV), sidestepping the gas-phase HV, extraction, and mechanical stability issues inherent in dual-phase TPCs (Juyal et al., 2021, Juyal et al., 2019). The main engineering bottleneck is controlling mechanical sag, tension, and field instabilities (e.g., continuous photon emission above $E(r) = V_A / [r\ln(b/a)]$1 MV/cm) over meter-scale anode lengths (Aprile et al., 2014, Tönnies et al., 2024). Needle-array configurations offer alternate topologies if uniform high fields and noise suppression can be maintained at scale (Knights et al., 2024).

6. Limitations, Backgrounds, and Comparison to Dual-phase TPCs

Single-phase S2 operation avoids the need for a liquid-gas interface, yielding full charge-extraction efficiency and mitigated drift-electron losses (Juyal et al., 2021, Juyal et al., 2019, Qi et al., 2024). However, achievable S2 gains ($E(r) = V_A / [r\ln(b/a)]$230 photons/e⁻) remain lower than dual-phase gas-gap gains ($E(r) = V_A / [r\ln(b/a)]$3 photons/e⁻), necessitating higher photodetection efficiency for low-energy thresholds.

Intrinsic limitations:

• Onset of "dark" discharge and spurious photon emission above $E(r) = V_A / [r\ln(b/a)]$4–$E(r) = V_A / [r\ln(b/a)]$5 MV/cm at the wire surface.
• Mechanical and tensioning challenges for long, thin anode wires.
• Modest charge multiplication; S2 gain $E(r) = V_A / [r\ln(b/a)]$6 is impractical with thin wires alone (Aprile et al., 2014).
• Single-electron backgrounds ("electron trains") persist, as demonstrated in single-phase TPCs (Qi et al., 2024).

Advantages relative to dual-phase include mechanical simplicity, simplified high-voltage architecture (no graded extraction grids or surface control), enhanced S1 collection (due to absence of total internal reflection at the liquid surface), and superior timing characteristics for S2 pulse discrimination (Kuger et al., 2021, Aprile et al., 2014). Energy and position reconstruction in large single-phase TPCs is tractable, with statistical S2-wide z-reconstruction sufficient for fiducialization and background rejection in sub-GeV dark matter searches (Kuger et al., 2021).

7. Prospects for Large-scale Applications and Future Development

The convergence of multi-group data (Waseda, CAL, SJTU, recent LXePSC and RTPC studies) on the field thresholds ($E(r) = V_A / [r\ln(b/a)]$7412 kV/cm), yields ($E(r) = V_A / [r\ln(b/a)]$810–30 photons/e⁻), and pulse shape proves the robustness of the underlying electrodynamics (Aprile et al., 2014, Juyal et al., 2019, Wei et al., 2021, Tönnies et al., 2024, Qi et al., 2023). Ongoing R&D focuses on:

• Scaling gain via further reduction in wire diameter and voltage optimization, balancing mechanical robustness and light-emission instabilities.
• Enhancing photon detection (e.g., via increased PMT/SiPM coverage or improved inner reflectivity) to compensate for lower intrinsic S2 yield.
• Advanced electrode schemes, including multi-point needle/ball arrays, to maintain high field regions across large LXe volumes with uniform performance (Knights et al., 2024).
• Suppression or characterization of field-induced photon emission and background sources to reach ultimate low-threshold sensitivity.

Single-phase LXe proportional scintillation is a viable and actively studied alternative to dual-phase architectures for next-generation dark matter and neutrino experiments, offering a path to simplified mechanics, sub-μs S2 timing, and enhanced discrimination, provided engineering and photon-collection constraints are systematically addressed (Aprile et al., 2014, Tönnies et al., 2024, Kuger et al., 2021, Qi et al., 2024, Juyal et al., 2021, Juyal et al., 2019, Qi et al., 2023, Wei et al., 2021, Knights et al., 2024).